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Homework Help: Propability of finding a particle outside the classical limit

  1. May 18, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm asked to calculate the propability of finding a particle outside the classical limit for a quantum harmonic oscillator in it's ground state

    2. Relevant equations
    Ψ0(x) = a*emωx2/2hbar
    When a = (mω/πhbar)1/4
    The ground state energy E0 =hbar*ω2/2
    3. The attempt at a solution
    I actually don't know what to do, I've tried to consider it as tunelling by finding when the energy is equal to the potential
    E0 = hbar*ω2/2 = mω2x2, and stuck there !
    And thank for your assistance
  2. jcsd
  3. May 18, 2015 #2


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    You might start by finding the amplitude, ##A##, of oscillation for a classical oscillator with energy E0. The quantum oscillator is "outside the classical limit" when x is outside the range ##-A\leq x \leq A##.

    I don't understand this equation. Why is ##\omega## squared in the middle expression. I also don't understand the meaning of the expression on the right.

    I think you have a typo in the expression for the wavefunction. The argument of the exponential should be negative.
    Last edited: May 18, 2015
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